A Physics-Constrained Framework for Fatigue Data Augmentation of Post-Weld Treated Joints: Censored S–N Estimation with an Exploratory Generative Component
A physics-constrained framework combining censored maximum-likelihood S–N estimation with an honestly-scoped generative component for fatigue data augmentation of TIG-dressed and HFMI-treated welded joints.
Overview:
This repository implements a physics-constrained computational framework for the analysis and augmentation of sparse fatigue databases for post-weld improved welded joints (TIG dressing and HFMI treatment). The methodology combines a unified preprocessing pipeline, a censored maximum-likelihood S–N estimator that retains run-outs as right-censored observations rather than discarding them, and a hard Basquin generation constraint that anchors every synthetic specimen to the S–N manifold. A Bayesian hierarchical pooling model, a Gaussian copula, and a conditional variational autoencoder (CVAE) are included as exploratory components — and are validated, not assumed, as such.
Unlike most fatigue-augmentation studies, this framework is built to answer a harder question than "can we generate more data?" — namely, does the generated data actually improve anything? Under group-level clustered inference and a structured component-removal ablation, only the physics-based Basquin constraint shows a statistically demonstrated positive effect on characteristic-strength accuracy. The conditional VAE degrades the estimate when that constraint is inactive, the copula contrast is not significant, and leave-one-study-out validation across 23 independent source studies shows no predictive benefit from augmentation at all. Two quantified, non-conservative defects — a 9.8% upward bias in characteristic strength from the generation-band filter, and generated scatter averaging only 0.83 of the experimental value — mean the synthetic data is explicitly restricted to exploratory and distributional analysis. It is not admissible for characteristic-strength or design-curve estimation, for which the censored fits to the experimental data should be used directly.
Key Challenges Addressed:
Data scarcity: as few as 9–50 specimens per detail–stress-ratio group, well below what unconstrained deep generative models typically need
Right-censored data: run-outs discarded by conventional S–N fitting shift characteristic strength by up to 74% when handled incorrectly
Severe population imbalance: HFMI populations up to 8.1× larger than TIG for the same joint geometry
Physical constraint violation: unconstrained generators (GAN, standard VAE) do not inherently respect the Basquin stress–life relationship
Honest scope-setting: distinguishing components with a demonstrated statistical benefit from those retained only as exploratory, and stating explicitly where synthetic data must not be used
Key Features:
Censored Maximum-Likelihood S–N Estimation: failures contribute a normal density, run-outs contribute a survival term — no run-outs discarded
Basquin Generation Constraint: the only component with a demonstrated positive effect on characteristic-strength accuracy (cluster-bootstrap contrast, two-sided p < 0.05)
Bayesian Hierarchical Pooling: non-centred parameterisation stabilising S–N slope estimates for groups as small as n = 9
Gaussian Copula Dependency Modelling: HFMI–TIG dependence structure, reported with its identifiability limits (7 of 17 detail–stress-ratio cells) made explicit
Conditional VAE Residual Generator: learns geometry-specific aleatory scatter conditioned on treatment type, geometry, and stress ratio — retained as exploratory, not as a proven predictive improvement
Structured Ablation Suite (Studies A–F): component-removal, physics-constraint-level, latent-dimension, stress-extension, residual-truncation, and hyperparameter sensitivity studies, each isolating one factor at a time
Explicit Scope Restriction: synthetic data is validated for exploratory and distributional use only, never for design-curve or characteristic-strength estimation
Applications:
The framework supports diverse applications across multiple domains:
Industrial Sectors:
Structural & Offshore Engineering: fatigue assessment of TIG-dressed and HFMI-treated welded steel structures
Bridge & Infrastructure: life extension analysis for welded steel bridges and industrial structures
Shipbuilding & Heavy Fabrication: design curve development for post-weld improved joints
Automotive & Rail: fatigue-critical welded component assessment across stress-ratio conditions
Research & Development:
Data Scarcity Research: a template for physics-constrained augmentation in any small-sample engineering domain
Generative Model Benchmarking: head-to-head comparison against WGAN-GP, standard VAE, bootstrap, KDE, and GMM baselines
Uncertainty Quantification: Bayesian hierarchical modelling with full MCMC convergence diagnostics
Methodology Development: a documented, reproducible case study in when generative augmentation does — and does not — help
Education & Benchmarking:
Teaching Tool: demonstrating rigorous ablation design and honest reporting of null and negative results
Benchmark Dataset: 1,476 specimens (965 HFMI, 511 TIG) across four standardised weld detail types
Reproducibility Reference: a verification suite (17 of 18 checks passing, with the one known limitation documented rather than hidden)
Validation:
The framework has been extensively validated against experimental data:
Dataset Size: 1,476 specimens after preprocessing (965 HFMI, 511 TIG), of which 1,361 are failures and 115 are censored run-outs
Materials: structural and high-strength steels, yield strength 235–960 MPa
Detail Types: butt joint, transverse attachment, longitudinal attachment, T-joint
Loading Conditions: two stress ratios spanning the IIW-recommended range
External Validation: leave-one-study-out across 23 independent source studies
Performance Metrics:
Physics constraint effect: significant positive characteristic-strength contrast under cluster-bootstrap inference (only significant positive contrast among all components tested)
Reference-band exceedance: reduced from 44.6% (unconstrained) to 8.8% with the full physics constraint active, against an experimental reference rate of 8.2%
Distributional fidelity: KS criterion met in 19 of 24 groups, Wasserstein criterion in 17 of 24
Leave-one-study-out RMSE: 0.4529 (unaugmented) vs. 0.4670 (augmented) — no predictive benefit demonstrated
Known non-conservative bounds: +9.8% average upward bias in characteristic strength from the generation-band filter; generated residual scatter averaging 0.83 of experimental scatter
Contributions:
Contributions to model enhancement, experimental validation, or industrial applications are welcome. Please contact the authors for collaboration opportunities.
Citation:
If this work supports your research, please cite the original paper:
@article{MULKOGLU2026FATIGUEAUG,
title = {A physics-constrained framework for fatigue data augmentation of post-weld treated joints: censored S{\textendash}N estimation with an exploratory generative component},
journal = {Journal of Intelligent Manufacturing},
year = {2026},
doi = {https://doi.org/10.1007/s10845-026-02975-4},
url = {https://link.springer.com/article/10.1007/s10845-026-02975-4},
author = {O{\u{g}}uzhan M{\"u}lko{\u{g}}lu and Melih Kandemir and Halid Can Y{\i}ld{\i}r{\i}m},
keywords = {Fatigue strength improvement, TIG dressing, HFMI treatment, Data augmentation, Physics-informed machine learning, Variational Autoencoder, Bayesian analysis, Welded joints},
abstract = {The fatigue performance of welded joints has been significantly enhanced through various post-weld improvement techniques, with Tungsten Inert Gas (TIG) dressing and High-Frequency Mechanical Impact (HFMI) treatment emerging as prominent methods. This study presents a physics-constrained computational framework for the analysis and augmentation of sparse fatigue databases. Its validated elements are a unified preprocessing pipeline, a censored maximum-likelihood S{\textendash}N estimator that retains run-outs as right-censored observations, a corrected stress-range extension, and a Basquin generation constraint that anchors every synthetic specimen to the S{\textendash}N manifold. Bayesian hierarchical pooling, a Gaussian copula and a conditional variational autoencoder are included as exploratory components and are reported as such. Under group-level clustered inference the Basquin constraint is the only component with a demonstrated positive effect on characteristic-strength accuracy; the conditional VAE degrades the estimate when that constraint is inactive, the copula contrast is not significant, and the copula is identifiable in only 7 of the 17 detail-stress-ratio cells. Leave-one-study-out validation across 23 independent source studies shows no predictive benefit from augmentation. Two quantified defects bound the scope of the generated data: the generation-band filter biases characteristic strength upward by 9.8% on average, and the generated residual scatter averages 0.83 of the experimental value. Both are non-conservative. The synthetic data is therefore restricted to exploratory and distributional analysis and is not admissible for characteristic-strength or design-curve estimation, for which the censored fits to the experimental data should be used directly.}
}
Basic Usage:
# Install dependencies
pip install -r requirements.txt
# Place source data files in the data/ directory
# HFMI_data.xlsx and TIG_data.xlsx
# Run the complete pipeline (preprocessing, S-N fitting,
# Bayesian correlation, augmentation, ablation studies,
# and verification)
bash run_all.sh
# Or run individual modules, e.g.:
python code/fatigue_preprocessing.py
python code/fatigue_stats.py
python code/ablation_study.py
python code/verify_pipeline.py
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